OFFSET
0,2
LINKS
Robert Price, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
Index entries for linear recurrences with constant coefficients, signature (0,21,0,-84,0,64).
FORMULA
Empirical a(n) = 21*a(n-2) - 84*a(n-4) + 64*a(n-6) for n>5. - Vincenzo Librandi, Dec 31 2015 and Apr 16 2019
Empirical g.f.: (1+3*x-17*x^2+48*x^3+16*x^4-96*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)). - Colin Barker, Dec 31 2015 and Apr 16 2019
Conjecture: a(n) = 2*(4^n - 2^n) - 1 for odd n; a(n) = 2^n for even n. - Karl V. Keller, Jr., Oct 03 2021
MATHEMATICA
rule=29; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 30 2015
STATUS
approved